Insights into the Origin of High Activity of Ni5P4(0001) for Hydrogen Evolution Reaction

Hydrogen evolution reaction (HER) is directly relevant to green hydrogen production from water splitting. Recently, a low-cost Ni5P4 material has been demonstrated experimentally and theoretically to exhibit excellent electrocatalytic activity toward HER. However, a fundamental understanding of the origin of Ni5P4(0001) activity is still lacking. In this work, density functional theory (DFT) calculations were employed for a comprehensive investigation. The calculation results indicate that the Ni5P4(0001) surface exposing Ni3P4 termination gains the highest stability, on which a nearly thermoneutral hydrogen adsorption was found at the P3-hollow sites, providing a high activity for HER. The activity was also observed to be maintained over a wide H-coverage. HER occurs via the Volmer–Heyrovsky mechanism as evidenced from the optimal hydrogen adsorption free energy, but unlikely through the Tafel reaction due to its large energy barrier. Furthermore, the P3-hollow sites also exhibit a low kinetic barrier for water dissociation, promoting HER in alkaline media. A series of electronic structure analyses were performed in gaining insights into the origin of the HER activity. First, the density of states (DOS) and crystal orbital Hamilton population (COHP) analyses revealed a favorable interaction of electronic states between P and H atoms, leading to stable H adsorption at P3-hollow sites. In addition, the Bader charge analysis demonstrates that the strength of H adsorption at P3-hollow sites linearly increases with the electrons carried by the latter. The optimal net charge on the P3-hollow sites leads to a desired ΔGH that is close-to-zero. Finally, a highly efficient electron transfer was observed between the P3-hollow sites and their neighboring atoms, facilitating the HER.


INTRODUCTION
Hydrogen can serve as the primary energy carrier of future energy systems due to its several distinct advantages such as high energy density and zero-carbon emission. 1−3 Electrocatalytic water splitting is an environmentally friendly way to produce green hydrogen sustainably by consuming the electricity generated from intermittent renewable energy sources (e.g., wind, hydro, tidal, and solar energy). 3−6 Hydrogen evolution reaction (HER) is an electrochemical half-reaction of water splitting. It requires high-performance electrocatalysts to proceed expeditiously, particularly under alkaline media where HER is more difficult but oxygen evolution reaction (OER, the other half-cell reaction in water splitting) is much more facile than those in acidic media. It has been recognized that the noble metals exhibit an excellent capability of efficiently catalyzing the HER. 7−9 However, their high cost and low earth abundance limit their application in large-scale green hydrogen production. 10,11 Therefore, it is essential to develop low-cost high-performance HER electrocatalysts. Ni 2 P > Ni 12 P 5 in acidic conditions. 24 In fact, Ni 5 P 4 has drawn great attention since it has been demonstrated to have HER activity comparable to the Pt. As reported by Laursen et al., in 1 M H 2 SO 4 solution, the Ni 5 P 4 exhibits a Tafel slope of 33 mV dec −1 and an overpotential of 62 mV at 100 mA cm −2 , which are close to the values given by Pt. 23 The high activity was also found on the highly ordered Ni 5 P 4 nanosheets with largely exposed surfaces synthesized by Ledendecker et al. 25 Besides, Ni 5 P 4 was even observed to be highly active under alkaline conditions where the HER is in fact more difficult compared to acidic media. 23,25,26 Moreover, it has been theoretically and experimentally indicated that the catalytic performance of Ni 5 P 4 is superior to that of other Ni-based compounds, e.g., Ni 3 S 2 and Ni 3 N. 27 Motivated by the excellent catalytic performance of Ni 5 P 4 , extensive efforts have been made to explore the origin of its activity for HER. One explanation given by a few researchers is that the Ni 5 P 4 has a higher positive charge over Ni atoms and a stronger ensemble effect of P atoms, which leads to an increased binding to the first H atom, and in turn enhances the affinity to the second proton. 24,28 However, the recent theoretical study has shown that the superior activity of Ni 5 P 4 (0001) is provided by the surface P atoms producing nearly optimal H adsorption, instead of the Ni atoms that bind strongly to the H adsorbates. 29 In a systematic study of the activity of Ni 5 P 4 surfaces for HER, Hu et al. confirmed the high activity of P atoms, and revealed a close correlation between the activity and the structural properties on an atomic scale. 30 However, there is still a lack of in-depth knowledge of the origin of this activity. In particular, there exist limited theoretical studies of the HER activity of Ni 5 P 4 in alkaline media and the underlying mechanism is still poorly understood. Although it is well-known that the electrocatalytic properties of materials are strongly related to the electronic structures of their surface atoms, 31−33 in the previous theoretical studies, the electronic nature of Ni 5 P 4 and its role in the HER activity have not been elucidated fully. Therefore, it is necessary to perform a comprehensive investigation to gain a deeper fundamental understanding of the inherent reasons underlying the high activity of Ni 5 P 4 for HER.
Herein, a comprehensive study has been conducted to understand the origin of the Ni 5 P 4 activity for HER through density functional theory (DFT) calculations. The low index (0001) facet of Ni 5 P 4 was chosen for the activity investigation because it has been experimentally demonstrated to be uniformly exposed. 29,34 The HER activity of Ni 5 P 4 (0001) was systematically evaluated, and the results show that the surface P atoms act as the active sites rather than Ni. This is in fact in good agreement with the previous finding. Through the transition state analysis, the reaction mechanism of HER on Ni 5 P 4 (0001) was determined and the performance of Ni 5 P 4 (0001) toward water dissociation was also explored. Furthermore, the role of the electronic structure of Ni 5 P 4 (0001) in the HER activity has been interpreted.

COMPUTATIONAL METHODS
The Vienna Ab initio Simulation Package (VASP) code based on density functional theory (DFT) was employed to perform the first-principles calculations. 35,36 The exchange-correlation energy was calculated by the generalized gradient approximation (GGA) of Perdew−Burke−Ernzerhof (PBE). 37 The interaction between electrons and ions (nucleus) was depicted with the projector augmented wave (PAW) method. 38 The van der Waals (vdW) interactions were described through the DFT-D3 method. 39 A high cutoff kinetic energy of 500 eV was applied for the plane-wave basis set to approximate the valence electron densities. The convergence criteria for energy and force were set to 10 −5 eV and 0.02 eV/Å, respectively. A (√3 × √3) R30°supercell of Ni 5 P 4 (0001) consisting of 108 atoms was constructed to explore the HER process on the surface. The vacuum layer thickness was set to 20 Å in the z-direction to eliminate the vertically periodic interaction. The slab dipole correction was applied to avoid the electrostatic effects along the z-direction. During structure relaxation, the atoms in the bottom Ni−P layers were frozen, and the number of frozen atoms varied with different surface terminations (Table S1). According to the Monkhorst−Pack scheme, the Brillouin zone was sampled by Γ-centered k-point meshes of 9 × 9 × 3 and 3 × 3 × 1 for the geometry optimization of the unit cell and supercells, respectively, while in the electronic structure calculations for them denser k-point meshes of 12 × 12 × 5 and 5 × 5 × 1 were used, respectively. The climbing image nudged elastic-band method (CI-NEB) was employed to search transition states. 40, 41 The vibrational frequency analysis was subsequently performed to confirm that only one imaginary frequency existed for the structures of the obtained transition states.
Due to the surface slabs of Ni 5 P 4 (0001) being asymmetric, the surface energy (γ) was calculated by the following expression: 42 where the E s unrelax and E s relax are the total energy of the unrelaxed and relaxed surface slabs, respectively; E b is the total energy of a unit cell of bulk Ni 5 P 4 ; N is the number of the unit cells contained in the surface slab; and A is the surface area of the slab model. The first term represents the energy consumed to cleave the bulk Ni 5 P 4 into two surface slabs, and the second term is the energy generated from the surface relaxation. The surface energy is the sum of the cleavage energy and the relaxation energy. 42 The Gibbs free energy for H adsorption (ΔG H ) is an excellent descriptor to evaluate the HER performance of one catalyst. 43 It can be obtained through the equation below: where ΔE H is the hydrogen adsorption energy, ΔZPE represents the zero-point energy correction of H adsorption, T is the temperature of 298 K, and ΔS H is the loss of entropy due to the adsorption of the hydrogen atoms on the catalyst surface. The ΔS H is approximated as ΔS H ≈ −1/2(S H2 0 ), where the S H2 0 is the entropy of H 2 in gas phase at standard conditions (298 K, 1 bar). The ΔE H can be calculated by the following equation: where E (n+1)H* and E nH* represent the total energy of the surface slabs with n+1 and n adsorbed H atoms, respectively; E Hd 2 is the energy of a hydrogen molecule in gas phase. The ΔZPE can be determined from where E TS and E IS represent the total energy of the transition state and initial state, respectively. In the electronic structure analysis, the net charge (Q net ) carried by an atom is defined as where Q bader and Q val are the calculated Bader charge and the number of valence electrons that the DFT calculations assume for the atom, respectively. A positive or negative value of the net charge represents that the atom loses or gains electrons (positively and negatively charged). The charge density difference (Δρ) for the H adsorption is defined as Δρ = ρ H+surf. − ρ surf. − ρ H , where ρ H+surf. , ρ surf. , and ρ H are the charge densities of the H-adsorbed surface, the clean surface, and the H atom, respectively.

RESULTS AND DISCUSSION
3.1. Structure and Stability of Ni 5 P 4 (0001) Surfaces. Figure 1a shows the structure of Ni 5 P 4 unit cell, which consists of 36 atoms and has a hexagonal structure with a space group of P6 3 mc. The optimized lattice constants are a = b = 6.729 Å and c = 10.890 Å, which are in good agreement with the reported experimental and computational results, as summar-  (a and b) Stable geometries of H adsorption at three kinds of sites on the Ni 3 P 4 -terminated Ni 5 P 4 (0001) surface. Note that a P 3 hollow can adsorb three H atoms, each of which bonds to one P atom of the P 3 hollow, while a Ni 3 hollow can only stabilize one H atom, bonding to the three Ni atoms, over the hollow center. The blue, red, and yellow spheres represent Ni, P, and H atoms, respectively. (c) Three-state free energy diagram for HER at the different surface sites. (d) Gibbs free energy of H adsorption as a function of the number of adsorbed H atoms at the P 3hollow site. (e) Gibbs free energy of H adsorption (ΔG H ) as a function of H coverage. The yellow region refers to the preferable range of ΔG H for HER (i.e., |ΔG H | < 0.2 eV). ized in Table S2. Figure 1b shows the calculated density of states (DOS) of the bulk Ni 5 P 4 . It can be observed that there are electronic states across the Fermi level, which are mainly contributed by the Ni atoms. This demonstrates that Ni 5 P 4 exhibits a metallic feature, facilitating electron transfer during electrocatalytic HER processes.
Analysis of surface stability was carried out to determine the most stable surface termination of Ni 5 P 4 in the [0001] direction. As presented in Figure 1a, the unit cell of Ni 5 P 4 is composed of two identical halves along the [0001] direction, one of which is rotated 180°around the (0001) axis with respect to the other one. In half a unit cell, the atoms have a complex arrangement in the [0001] direction and the delineation of atomic layers is less clear. By removing the outermost atoms or atomic layers from the surface in the [0001] direction, as illustrated in Figure S1, five possible surface terminations were obtained. According to the composition of the exposed surface atoms, they are referred to as Ni 3 P 4 , Ni 3 P 3 , Ni 7 P 3 , Ni 4 P 3 , and Ni 3 P 5 surface terminations, respectively. Figure 1c shows a comparison of the calculated surface energy of the Ni 5 P 4 (0001) with different terminations. It is clearly demonstrated that the Ni 3 P 4terminated Ni 5 P 4 (0001) has the lowest surface energy, which implies that Ni 3 P 4 is the most stable termination. By energetics consideration, it is predicted that the Ni 3 P 4 termination has a high probability of being exposed to the reactant during HER catalysis. 44 Therefore, the Ni 3 P 4 termination was selected to investigate the catalytic activity of Ni 5 P 4 (0001) for HER. Figure 2a, the Ni 3 P 4 -terminated Ni 5 P 4 (0001) surface consists of repeating triangular Ni 3 connected with each other by tetrahedral P 4 . The P corners of three adjacent tetrahedral P 4 gather around a common point, creating a P 3 hollow. We have considered all possible sites on the Ni 3 P 4 termination to identify stable hydrogen adsorption sites. After full structure relaxation, the H adsorption was finally stabilized at three types of sites, i.e., Ni 3 -hollow sites, P-top sites (the top of central P in tetrahedral P 4 ), and P 3 -hollow sites. The optimized geometry of H adsorption for each kind of site is schematically demonstrated in Figure 2a and 2b. It has been found that a P 3 -hollow site can accommodate three H atoms, each of which bonds to one P atom there, while a Ni 3 -hollow site can stabilize only one H atom, bonding to the three Ni atoms, over their center. According to the calculated H adsorption energy (ΔE) listed in Table S3, the Ni 3 -hollow sites are identified as the preferable sites for H adsorption with the largest negative ΔE value of −0.732 eV, whereas the P 3 -hollow sites and P-top sites exhibit relatively weaker adsorption toward H atoms than the Ni 3hollow sites, with much smaller negative ΔE value of −0.276 eV and −0.422 eV, respectively.

HER Activity of Ni 5 P 4 (0001) with Ni 3 P 4 Termination. As shown in
The Gibbs free energy of H adsorption (ΔG H ) has been generally perceived as a suitable descriptor for evaluating HER performance. The ΔG H should be close to zero on excellent HER electrocatalysts, which indicates an ideal trade-off between adsorption and release of H atoms during surface electrocatalysis. Either too weak or too strong binding of H atoms to the catalyst surface can lead to an inefficient HER process. Figure 2c and Table S3 show the calculated ΔG H for the Ni 3 P 4 -terminated Ni 5 P 4 (0001) surface. The P 3 -hollow sites have a nearly thermoneutral H-adsorption with a ΔG H value of 0.012 eV that is close-to-zero, signifying that the P 3 -hollow sites can deliver near-optimal HER catalytic activity. The P-top sites are also highly active for HER (ΔG H = −0.121 eV), but their activity is lower than P 3 -hollow sites. The biggest negative ΔG H (−0.484 eV) was found for Ni 3 -hollow sites. With such a large negative ΔG H , the H atoms can be readily adsorbed at the Ni 3 -hollow sites, but the release of H atoms from these sites is very difficult, leading to an inefficient HER process. In addition, given that each P 3 -hollow site can adsorb two additional H atoms, we investigated the effect of the number of adsorbed H atoms at one P 3 -hollow site on its HER activity. As shown in Figure 2d, the adsorption of the second H atom becomes easier with a more negative ΔG H . However, when one more (i.e., the third) H atom is adsorbed at the site, the ΔG H is increased to 0.046 eV, more positive than that of the adsorption of only one H atom. This indicates that the activity of the P 3 -hollow site is diminished due to the interactions among adsorbed H atoms when the site is fully occupied by three H atoms. Despite that, this ΔG H value of 0.046 eV remains close to zero, demonstrating that the high catalytic activity of the P 3 -hollow site for HER can be maintained with the increasing number of the adsorbed H atoms at the site.
Furthermore, we explored the dependence of the HER activity of Ni 3 P 4 -terminated Ni 5 P 4 (0001) surface on H coverage. The H coverage is defined as the ratio of the number of adsorbed H atoms to the number of surface adsorption sites. Since the above results suggest that the interaction of the adsorbed H atoms at the P 3 -hollow sites can affect the ΔG H , we considered two pathways (A and B) for increasing the H coverage at the P 3 -hollow sites, as schematically illustrated in Figure S2. In pathway A, the H atoms are adsorbed at one P 3 -hollow site until the latter is fully occupied, then another P 3 -hollow site begins to adsorb H atoms, while in pathway B, the adsorption of the next H atom always occurs at another P 3 -hollow site. At a same H coverage (at least two H atoms are adsorbed at the same P 3 -hollow site), there are different interactions of H atoms at P 3 -hollow sites in the pathways A and B. Figure 2e and Table S4 show the calculated ΔG H values under various H coverages in the pathways A and B. The yellow region in Figure 2e refers to the preferable range of Gibbs free energy of H adsorption (|ΔG H | < 0.2 eV). 45 Clearly, pathway A has greater ΔG H values than pathway B between 7/15 and 9/15 H-coverage due to the stronger interaction of adsorbed H atoms at the P 3 -hollows in pathway A. Subsequently, at 10/15 H-coverage, the ΔG H value of pathway A is greatly reduced to a value lower than that of pathway B. This is because, for 10/15 H-coverage, the Hadsorption via pathway A occurs at the nonoccupied P 3 -hollow site, while in pathway B the P 3 -hollow site is already occupied by one H atom. This leads to stronger interaction between the adsorbed H atoms in pathway B than in A, weakening the H adsorption. Between 46 The Volmer−Heyrovsky pathway is also viable at P-top sites, but their HER rates are relatively lower than the P 3 -hollow sites since the P-top sites have a less favorable Heyrovsky step. Regarding the Ni 3 -hollow sites, their strong binding to the H atoms favors the Volmer step but in the meantime makes it difficult to release the adsorbed H atom to produce H 2 , hindering the Heyrovsky step.  The Tafel step is a process in which two adsorbed H atoms combine to produce a H 2 molecule. One of the reasons for the excellent HER performance of Pt catalysts is that they have a fast Tafel step; 47 thus, we explored the viability of the Tafel step on the Ni 3 P 4 -terminated Ni 5 P 4 (0001) surface. Due to the P 3 -hollow sites being the main active sites for HER, we calculated the energy barriers of the Tafel reactions at the P 3hollow sites. As shown in Figure 3, we considered two kinds of H adsorption configurations at P 3 -hollow sites as the beginning of the Tafel reaction. One is the P 3 -hollow site partially occupied by two H atoms, while the other is fully occupied by three H atoms, two of which subsequently combine to form H 2 . However, both cases were found to possess high energy barriers of 1.235 and 1.222 eV, suggesting the sluggish kinetics of H 2 generation at the P 3 -hollow sites through Tafel reactions. A previous study by Ling et al. 48 has shown that a greatly reduced H−H distance between two neighboring adsorbed H atoms can lead to a low energy barrier for the Tafel reaction. In their study, a very low energy barrier of 0.48 eV for the Tafel reaction was obtained at those active sites where the two adsorbed H atoms are about 1.5 Å apart, while, in our work, the H−H distances are found to be much greater, 2.20 and 2.19 Å for both H adsorption configurations, respectively. Therefore, we believe that the long H−H distance between two adjacent adsorbed H atoms at the P 3 -hollow sites is a crucial factor causing their high kinetic barriers for Tafel reactions. Overall, it can be concluded that in acidic environments the energetically favorable Volmer−Heyrovsky pathway is the dominant mechanism for the HER on the Ni 3 P 4 -terminated Ni 5 P 4 (0001) surface. This is in agreement with the experimental result that a Volmer−Heyrovsky mechanism for Ni 5 P 4 was indicated by the obtained Tafel slope of 40 mV dec −1 . 25 Due to the scarcity of protons in alkaline electrolytes, water dissociation, also known as the alkaline Volmer step (H 2 O + e − → H* + OH − ), becomes the main source providing H intermediates. Therefore, the kinetic barrier for water dissociation was examined for the Ni 3 P 4 -terminated Ni 5 P 4 (0001) surface. It was found that on the surface there were two kinds of sites for stable adsorption of molecular water, i.e., P 3 -hollow and Ni 3 -hollow sites. Figure 4a and 4b show the stable geometries of the water molecule adsorbed at P 3 -hollow and Ni 3 -hollow sites, respectively. The adsorption energy was calculated to be −0.183 eV and −0.289 eV on the P 3 -hollow and Ni 3 -hollow sites, respectively, suggesting that the Ni 3 -hollow sites have a stronger adsorption for H 2  The transition state analysis was then performed to determine the energy barriers for water dissociation at P 3hollow and Ni 3 -hollow sites. Figure 4c and 4d show the energy changes as a function of the reaction coordinate, together with the schematic representations of the initial state (IS), transition state (TS), and final state (FS) of water dissociation at P 3hollow and Ni 3 -hollow sites, respectively. It can be observed that the water dissociation at both sites is exothermic, indicating a thermodynamically favorable process. In addition, the energy barrier for water dissociation at Ni 3 -hollow sites (1.241 eV) is much higher than at P 3 -hollow sites (0.404 eV). This is because at the P 3 -hollow site, the H and OH species generated from water dissociation can be directly captured by the P 3 -hollow site at once. However, since the Ni 3 -hollow site can only adsorb one H atom, the generated OH specie needs to diffuse to the P 3 -hollow site to be stabilized. Although the Ni 3 -hollow site can activate the O−H bond in H 2 O more favorably during H 2 O adsorption, the diffusion of the OH species on the surface inevitably introduces an extra kinetic barrier, resulting in an increase in the energy barrier for H 2 O dissociation at the Ni 3 -hollow site. Therefore, the H adsorbate can be preferentially generated at P 3 -hollow sites during water dissociation, favoring the alkaline HER. Besides, the energy barrier for water dissociation on Ni 5 P 4 (0001) (0.404 eV) is much lower in comparison to that on Ni 2 P (0.82 eV) reported by Cross et al. 49 This is in accordance with the experimental finding that Ni 5 P 4 exhibits a higher catalytic activity for alkaline HER than Ni 2 P. 23

3.4.
Origin of Ni 5 P 4 (0001) Activity for HER. The above results have indicated that the P 3 -hollow sites of the Ni 3 P 4terminated Ni 5 P 4 (0001) surface exhibit a superior activity for HER. To gain insight into the origin of the activity of P 3hollow sites, a series of electronic structure analyses were performed. We first investigated the bonding characteristics of the P 3 -hollow site with H adsorbates. Figure 5a depicted the calculated density of states (DOS) of the P 3 -hollow site before and after H adsorption. It can be seen that after H adsorption the total DOS is reduced around the Fermi level. Besides, the total DOS below the Fermi level shifts downward to lower energy, while a localized peak is formed at a higher energy above the Fermi level. These changes can be explained by the underlying mechanism of bond formation. When the H atom approaches the P 3 -hollow site on the surface, the coupling of electronic states between them leads to the hybridized energy levels, shifting downward to form bonding states and shifting upward to form antibonding states. The bonding states are well below the Fermi Level and thus fully filled, while the antibonding states are usually located across the Fermi Level and thus partially filled. The adsorption strength is strongly associated with the filling of antibonding states. To intuitively demonstrate the bonding and antibonding states for the P−H bond, the projected crystal orbital Hamilton population (pCOHP) analysis was performed. As shown in Figure 5b, the bonding states of the P−H bond are positioned well below the Fermi level and are thus fully filled. Most of antibonding states are above the Fermi level, while only a small fraction of antibonding states is below the Fermi level, indicating that few antibonding states are filled. This favorable interaction of electronic states leads to the P 3 -hollow site producing stable adsorption toward H atoms during the HER process.
Next, we investigated the effect of the net charge (defined by eq 7) carried by the P 3 -hollow site on its HER activity by means of Bader charge analysis. To adjust the net charge of the P 3 -hollow site, the strategy of exploring substitutional doping by nonmetal atoms was employed here. As illustrated in Figure  6a, the central P atoms of the tetrahedral P 4 on the Ni 3 P 4 termination were substituted by various nonmetal atoms, i.e., B, C, N, O, Si, and S. The electronegativity of these nonmetal atoms follows the order of O > N > S > C > P > B > Si. Figure  S3 presents the optimized geometries of the doped Ni 3 P 4terminated Ni 5 P 4 (0001) surfaces. It can be seen that the structures of these doped surfaces remain consistent with the pristine surface, except for the O-doped surface, where a significant structural distortion occurs due to the strong electronegativity of O atoms. Therefore, doping of O atoms is not considered in the following analysis. As observed in Figure  6b, the net charge of the P 3 -hollow site presents a clear linear relationship with the electronegativity of the central atoms. This indicates that the electronegativity difference between the doped atom and P successfully evokes the charge redistribution  The Journal of Physical Chemistry C pubs.acs.org/JPCC Article and modulates the net charge of the P 3 -hollow site. Specifically, the dopant atoms (O, N, S, and C) with a higher electronegativity than P make their surrounding P atoms at P 3 -hollow sites more positively charged as they attract the electrons from the latter, and vice versa. The adjusted net charge ranges from −0.398 to 0.478 e. The highest and lowest net charges are given by the doping of Si and N atoms, respectively. The ΔG H of P 3 -hollow sites on the doped surface was calculated to assess their HER activity. As shown in Figure  6c, the doping of Si atoms gives the most negative ΔG H of −0.083 eV at P 3 -hollow sites while the most positive ΔG H (0.105 eV) is found for the N doping. This shows that the ΔG H values at the P 3 -hollow sites on the doped surfaces remain within the preferable Gibbs free energy range (|ΔG H | < 0.2 eV) for the HER, as already mentioned above. Besides, the ΔG H is linearly correlated with the net charge with a reasonable fitting factor R 2 of 0.89. A larger negative net charge is observed to generate a more negative value of ΔG H , which implies that the P 3 -hollow sites with more electrons can provide stronger adsorption toward H atoms. Importantly, it can be seen that the P 3 -hollow sites on the pristine surface have an optimal net charge that leads to the nearly thermoneutral H adsorption. This is responsible for the superb activity of the pristine Ni 3 P 4 -terminated Ni 5 P 4 (0001) surface for HER. Furthermore, charge transfer analysis was also performed to understand the adsorbate−surface interaction. Figure 7a shows the charge density difference of the Ni 3 P 4 -terminated Ni 5 P 4 (0001) surface before and after H adsorption. It can be observed that the H adsorption at the P 3 -hollow site triggers a significant charge transfer; i.e., there is noticeable electron depletion (green) around the P 3 -hollow site and the H atom, while electron accumulation in the middle between the two atoms. This indicates the strong interaction between the two atoms and the formation of the P−H bond during H adsorption, in agreement with the DOS and pCOHP analyses described above. Another region of electron depletion is found under the P 3 -hollow site, and the electrons move toward the P 3 -hollow site. The direction of this charge transfer can be attributed to the P 3 -hollow site gaining electrons from the surroundings to balance its reduced charge during the formation of the P−H bond. Besides, an obvious charge transfer between the P 3 -hollow site and the surrounding Ni atoms also occurs. This corresponds to the observed increase in the lengths of the Ni−P bonds after H adsorption ( Figure  S4), which indicates the weakened strength of neighboring Ni−P bonds.
To further understand the effect of charge transfer on the HER activity of P 3 -hollow sites, we now discuss the Ni 3 P 4terminated Ni 5 P 4 (0001̅ ) surface since we found that the activity of P 3 -hollow sites on this surface suffers from poor charge transfer. It is worth noting that although the Ni 5 P 4 (0001) and Ni 5 P 4 (0001̅ ) surfaces have the same termination of Ni 3 P 4 composition, they are still structurally distinct, due to the bulk Ni 5 P 4 lacks mirror symmetry along the [0001] direction, as illustrated in Figure S5. We refer to the two surfaces as (0001)-Ni 3 P 4 and (0001̅ )-Ni 3 P 4 in the following discussion, respectively. The net charge of the P 3hollow site on the (0001̅ )-Ni 3 P 4 is calculated to be −0.151 e, more negative than that on the (0001)-Ni 3 P 4 (−0.075 e). However, the P 3 -hollow site on the (0001̅ )-Ni 3 P 4 (ΔG H = 0.317 eV) exhibits a much weaker ability toward H adsorption than the (0001)-Ni 3 P 4 (ΔG H = 0.012 eV), which is apparently inconsistent with the above result that the higher net charge of the P 3 -hollow site can generate stronger H adsorption. After examining the charge distribution on the surface, we found that the central P atom of the tetrahedral P 4 on the (0001)-Ni 3 P 4 is positively charged with a net charge of 0.069 e. This leads to the central P atom, as a nonmetal element, having stronger attraction to electrons. For instance, Figure 7b shows a significant charge transfer occurs between the P 3 -hollow site with the neighboring atoms after H adsorption. The Bader analysis (Figure 7c) indicates that after the first H atom is adsorbed at the P 3 -hollow site, the net charge of the central P atom increases by 0.068 e. Clearly, this unfavorable charge transfer prevents the P 3 -hollow site from gaining enough electrons to form a stronger P−H bond. On the other hand, the adsorption of the first H atom makes the central P atom less positively charged (0.001 e), weakening the attraction of the central P atom toward electrons. Thus, upon the adsorption of the second H atom, the central P atom attracts fewer electrons (Figure 7c); i.e., the net charge of the central P atom decreases from 0.001 to −0.001 e, lowering the ΔG H to 0.244 eV and favoring the H adsorption at the P 3 -hollow site. With the central P atom turning to be negatively charged, the central P atom does not attract electrons from the surrounding atoms but acts as an electron donor to provide the electrons for the P 3 -hollow site to bind to the H adsorbate. This leads to ΔG H being further reduced to 0.142 eV, signifying the much easier adsorption of the third H atom. Compared with the (0001̅ )-Ni 3 P 4 surface, the (0001)-Ni 3 P 4 surface has a favorable charge distribution, benefiting the charge transfer. For example, the central P atom is negatively charged with the net charge of −0.012 e on the clean (0001)-Ni 3 P 4 surface. After the adsorption of one H atom, the net charge is increased to −0.005 e and the central P atom remain negatively charged. This demonstrates that the central P atom can remain as an electron donor to the P 3 -hollow site to promote the H adsorption. Therefore, the (0001)-Ni 3 P 4 surface has a favorable charge transfer, facilitating the HER process.

CONCLUSIONS
DFT calculations were successfully performed to investigate the origin of the HER activity of Ni 5 P 4 (0001) model catalyst. The results show that the lowest surface energy was obtained on the Ni 5 P 4 (0001) surface exposing Ni 3 P 4 termination. The P 3 -hollow sites provide thermoneutral hydrogen adsorption, thus contributing to the high HER activity of Ni 5 P 4 (0001). It has also been observed that the surface remains catalytically active over a wide H coverage. The optimal free energy for hydrogen adsorption suggests that HER is facile via the Volmer−Heyrovsky mechanism, while the Tafel reaction is kinetically unfavorable due to its large energy barrier. The P 3 hollow sites were also found to provide a low energy barrier toward water dissociation, favoring the alkaline HER. A series of electronic structure analyses performed have gained a deeper understanding of the activity origin. The results indicate that the superior HER activity of Ni 5 P 4 (0001) can be attributed to three main factors. First, the DOS and COHP analyses revealed a favorable interaction of electronic states, leading to stable adsorption of P atoms toward H atoms. Second, from the Bader charge analysis, it was found that the strength of H adsorption at P 3 -hollow sites linearly increases with the electrons carried by them. The appropriate net charge at P 3 -hollow sites leads to the optimal close-to-zero ΔG H . Third, highly efficient electron transfer between the P 3 -hollow